Final answer:
The problem is solved by finding the total weight of products from two machines and distributing this weight into 2kg and 7kg boxes. The correct combination that fits the total weight of 72kg is 16 boxes of 2kg and 6 boxes of 7kg packaging, which corresponds to answer option D.
Step-by-step explanation:
To solve this problem, we need to calculate how many 2kg and 7kg packages can fit into the total weight produced by the two machines. First, let's find the total weight. The first machine produced 40.25 kg and the second machine produced 31 3/4 kg, which is 31.75 kg when converted to decimal. So, the total weight is 40.25 kg + 31.75 kg = 72 kg.
We'll need more than 100 words to explain the entire process of distributing the product into 2kg and 7kg packaging boxes. Let's assume the number of 2kg boxes is x and the number of 7kg boxes is y. The total weight can be described by the equation 2x + 7y = 72.
Since we're dealing with whole numbers, we can try different combinations of x and y to see which one matches the total weight of 72 kg. After checking all options, we find that 16 boxes of 2kg and 6 boxes of 7kg give exactly 72 kg (32kg + 42kg). Therefore, the correct answer is D) 16 boxes of 2kg packaging and 6 boxes of 7kg packaging.